History of Topics in Special Relativity/Three-acceleration

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Overview[edit | edit source]

The Lorentz transformation of three-acceleration is given by

or in vector notation in arbitrary directions

History[edit | edit source]

Poincaré (1905/06)[edit | edit source]

w:Henri Poincaré (July 1905, published January 1906) introduces the Lorentz transformation of three-acceleration:[R 1]

where , , , .

Einstein (1907/08)[edit | edit source]

w:Albert Einstein (December 1907, published 1908) defined the transformation by restricting himself to the x-component (apparently due to a printing error, Einstein's expresson misses a cube in the denominator on the right hand side):[R 2]

.

Abraham (1908)[edit | edit source]

w:Max Abraham derived the transformation for three-acceleration by differentiation of the velocity addition in x an y direction:[R 3]

or simplified by defining vector :

Laue (1908)[edit | edit source]

w:Max von Laue wrote the transformation for three-acceleration as follows:[R 4]

Brill (1909)[edit | edit source]

w:Alexander von Brill wrote the formulas in terms of motions in z-direction:[R 5]

Tamaki (1913)[edit | edit source]

w:Kajuro Tamaki was the first to write the formula in three-vector notation:[R 6]

and went on to decompose the acceleration into two component vector, one in the direction of and the other perpendicular to it:

References[edit | edit source]

  1. Poincaré (1905/06), p. 160
  2. Einstein (1907/08), p. 432
  3. Abraham (1908), pp. 375-376
  4. Laue (1908), p. 840
  5. Brill (1909), p. 210
  6. Tamaki (1913), p. 242
  • Abraham, M. (1908). Theorie der Elektrizität: Elektromagnetische Theorie der Strahlung; 2. Auflage. Leipzig: Teubner. https://www.archive.org/details/theoriederelekt00fpgoog. 
  • Brill, Alexander (1909). Vorlesungen zur Einführung in die Mechanik raumerfüllender Massen. Leipzig. https://rcin.org.pl/dlibra/publication/13858. 
  • Einstein, Albert (1908) [1907], "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen", Jahrbuch der Radioaktivität und Elektronik, 4: 411–462, Bibcode:1905AnP...322..891E, doi:10.1002/andp.19053221004. See also: English translation.
  • Laue, Max von (1908). "Die Wellenstrahlung einer bewegten Punktladung nach dem Relativitätsprinzip". Berichte der Deutschen Physikalischen Gesellschaft: 838-844. http://www.archive.org/details/verhandlungende39unkngoog.